click to enlarge

Illustration 1
Marcel Duchamp, Note from
the Green Box, 1934
(typographic version by Richard
Hamilton, translated by George
Heard Hamilton, 1960)

Duchamp states innotes written between 1911-15 (see illustration 1, showing Duchamp’sGreen Box Note published in 1934) that the time and date of hisreadymades is important “information” in addition to the “serialcharacteristic of the readymade.”⁽¹⁾

The “snapshoteffect”⁽²⁾of this timing of the readymade, to which Duchamp refers in this note,makes sense when we examine Duchamp’s readymades with his mathematicalnotes (written 1911-15 but held back for publication by Duchamp until1967, a year before his death.)⁽³⁾

First, let us begin by “looking” at Duchamp’s readymades through time. Since Duchamp claims that he “lost” most of his original readymade objects, Duchamp’s 1915 hatrack, as well as his urinal, snow shovel, coatrack, bottlerack and bicycle wheel and stool, exist only in a series of varied representations given to us by Duchamp over an extended period of time.

As an example, the following time-line illustrates the sequence of appearances of Duchamp’s “lost” hatrack. We see “the serial characteristic of the Readymade” just as Duchamp described in a presentation of his “Readymade” (the title he used for his hatrack in the 1941 representation, see illustrations 2A, B, C, D, E, and F below).

Time Line of Readymade Series of Hatracks – As Seen by Spectators
2A	2B	2C	2D	2E	2F
Click each image to enlarge
1918	1941	1960s (made 1916-17 found 1960s)	1960s (made 1918 found 1960s)	1964	1991 (made 1964 seen 1991)
2D Shadow in Oil Paint Tu m’ (detail)	2D Print made with Photo Boite-en-Valise	2D Photo Studio Photo	2D Shadow in Photo Cast Shadows (detail)	3D Wood Model Hatrack (limited edition of 8)	2D Blueprint Hatrack

Thus the tally of Duchamp’s hatrack representations is as follows:

2 2D shadows
(one painted [1918, Tu m’]; one photographed [1918, Cast Shadows])

2 2D photographic images
(one made into a print [1941, Boite-en-valise]; and one altered studio photograph [1916-17, found in 1960s]. Note both photographs are altered — to be discussed later in this essay.

1 2D blueprint (1964)
that, one assumes, generated
1 3D wood model (1964)
(in an edition of 8)

In effect, Duchamp gives us only 6 “snapshots” in time of his Hatrack Readymade (with “all kinds of delays”)⁽⁴⁾.The limited total of information that we have, obviously, does not equal the quantity of data that we would have if we had access to the lost 3D original or if we suddenly possessed many more 2D photographs that carefully depicted the original 3D hatrack “in the round.”

Indeed, with the paltry set of data that Duchamp provides, the only physical or mental construction we can make, based upon the hatrack’s original form, is by fusing or averaging and filling in among the 6 representations previously listed — 5 images in 2D and 1 model in 3D. This procedure can be done mentally via visualization, or physically via model-making, with conscious effort on the part of spectators. However, interpreting 2D depictions, mentally translating them into 3D, and then rotating and joining them (with visual filling in), is not a skill equally possessed by everyone and has, in fact, been frequently used as one measure of intelligence.⁽⁵⁾

Alternatively, if we do not help ourselves by consciously combining the 6 hatrack depictions, the result is an ad hoc, automatic conclusion or assumption-generated “readymade” from the unconscious mind. A single depiction — such as the first Duchamp hatrack that we see in a photograph or a print, or the 3D Schwarz model, or any one of a combination of Duchamp’s 6 particular depictions — has served to evoke in our minds a “general idea of a Duchamp hatrack” that is surely derived from an uncertainmixture taken from among Duchamp’s 6 hatrack representations and our prior experience with hatracks.

But does our present “generalization” or “knowledge” of Duchamp’s hatrack hold up to testing? In other words, will the generality that we have made about Duchamp’s readymades, and have long held inour minds and in our written art history — that such readymades as the hatrack are simply store bought, unaltered, mass produced objects — be maintained after more snapshots are added to the 6 that we havealready tallied. Yet, you may challenge: how can we add more snapshots to our generality when Duchamp gives us only 6 representations and the original is lost?

Herein lies the key to Duchamp’s insight, conveyed within his In the Infinitive [a.k.a. the White Box](1967) mathematical notes (1911-15). After identifyingthe 6 representations that Duchamp has given us as 6 distinct and separate snapshot views of his original hatrack, we have, essentially, a set of 6 “cuts” or 2D parts taken from a larger set of information,or the hatrack as a 3D whole. These 6 “cuts” are, in essence, 6 perspective views or observations. Each cut is also, itself, an “aggregate” (made of parts) of additional “cuts” or observations — ad infinitum. In other words, to add more cuts to our set of 6 hatrack representations, we must simply repeat our previous operation. Just as we took 6 cuts (parts), beginning from our generality of Duchamp’s hatrack, we must now take these 6 cuts (now themselves a set or whole) and cut each of these cuts into more cuts.

click to enlarge

Illustration 3A, 3B
Marcel Duchamp, Note from
In the Infinitive
[a.k.a. the White Box], 1967
Note: labels 3A and 3B
are for clarity added by author

Duchamp clearly indicates his grasp of this recursive nature of our mental operations in the White Box Notes. Several drawings illustrate two perspectives that behave as one process split into two alternating mental states. Our perspectives mechanically move back and forth between the general (a single perspective of the AGFC figure, see illustration 3A) to the particular (multiple snapshots [cuts] or perspectives of A,G,F,C in a series over time, see illustration 3B). Immediately after perspectives A,G,F and C are cut as in figure 3B, we have created a new set that functions as a generality, as in figure 3A.We then begin the cycle all over again, with more cuts of this generality,then another generality, then cuts in a series, again at finer and finer scales. Essentially, we are mentally and observationally moving back and forth between states 3A and 3B — wholes and parts at different levels of details.

Illustrations 4A and 4B show how the schematic diagram of Duchamp’s two mental operations contained in illustration 3A and 3B apply to his hatrack. Illustration 4A matches the relation of the single perspective in 3A (Here Duchamp’s hatrack in particular, and prior experience of hatracks in general, are fused together), whereas illustration 4B matches the relation of a series of perspectives taken over time as in 3B (Where Duchamp’s hatracks are reduced to multiple but discrete snapshots in a time-series). Illustration 4C depicts a possible series of mental steps that could occur immediately after 4B. This series illustrates how we now cut each of the 6 cuts from step 4B into more cuts, at an even finer scale of observation, ad infinitum.

click images to enlarge

Illustration 4A.


Illustration 4B.

Illustration 4C.


As in 3A and 4A above
Step 1whole generalization
Single perspective of set 6 Duchamp Hatracks fused with observer’s prior experience.

As in 3B and 4B above
Step 2whole cut into parts
Multiple perspectives (cuts) of 6 Duchamp Hatracks fused with observer’s prior experience.

As in 3A and 4A
Step 3-Hatrack parts (cuts) now are their own whole.

As in 3B and 4B
Step 4
This new Hatrack whole is also cut into parts(finer scale observation)

As in 3A and 4D
Step 5
This Hatrack part is now seen as one whole
As in 3B and 4B
Step 6
This whole hatrack part is also cut into more parts–ad infinitum

Step 4 of illustration 4C above answers the challenge previously mentioned: how do we add more cuts to our limited set of 6 representations of Duchamp’s hatrack?

click to enlarge

Illustration 5
Cube seen in 2D parts
as eye moves around it

Illustration 6
Perspective distortions of cube
in relation to fixed eye

When we actually take Duchamp’s hatracks representations and add the cuts (beyond merely identifyingthe 6 snapshots as in step 2 in illustration 4C), we discover that everyone of the 6 representations (5 in 2D and 1 in 3D) is not, as we mighthave expected, a single cut from the same 3D hatrack object. By wayof example, see illustration #5, if we reassemble all observations (cuts)resulting from the set of all eye positions looking at this particularcube, we would be able to predict, and easily to build, a symmetricalcube object from the resulting limited set of cuts. Each cut, upon examination,fulfills our expectation of a cube’s form with its 6 faces, 12 edges8 vertices — all we have to do is just count them to confirm. Illustration#6 depicts how the perspective distortions change according to the angleof eye’s observation of the cube.

Our expectations arenot fulfilled upon examining the 6 hatrack snapshots. Not only are thecurvatures of the hooks different in all 6 representations, but we mustconclude that even the number of hooks varies after we count them. Forexample, the Schwarz 3D model, (the “corrected” second version)has 6 equal length hooks, symmetrically placed as 3 on one side and3 on the other side of the base’s circular form. In contrast, the blueprint(approved and signed “okay, Marcel Duchamp”) has a weird tangleof 2 long and 3 short hooks.

click images to enlarge

Click here for Interactive Presentation
(Shown below at only 60% of actual size)

To download the plug-in, click here

Interactive Software Instructions:

Please test out the interactive hatrack software thatwe have installed⁽⁶⁾.To select a hatrack click on one of the 5 icons shown on the upper left.Hold the left side of the mouse down. Making sure the cursor’s handicon switches on (while the arrow is moving) roll the mouse on the hatrack’sround base and “pull” the 3D model off its fixed position in the 2Drepresentation. Interactive challenges include; the 1941 print of astudio photo (and an early stage of our hatrack 3D computer model),the 1917-18 studio photo (and an early stage of our hatrack 3D computermodel), the 1964 Schwarz blueprint (with a computer model of the Schwarz3D version), the 1964 Schwarz blueprint (with an early stage of ourhatrack 3D computer model) and, a 1904 Thonet hatrack catalogue diagram(and equivalent 3D computer model)⁽⁷⁾.To explore these 5 models, keep the left side of the mouse down, (alwaysbeginning with the hatrack’s base) and roll the mouse in various directions,and compare the 3D shape of the hatrack to the 2D representation. Rotateeach of the 5 hatrack 3D models in all x, y and z directions that arepossible in 3D space (north, south, east, west, up and down). Try tovisualize the 2D representation that you choose as a 2D slice (cut),or only one fixed perspective view of the 3D hatrack form. Also, practiceplacing the 3D models back into the best possible position matchingthe 2D depiction you have chosen.

The 5 computer modelsshown in the hatrack interactive design result from early stages ofour geometric analysis of the 6 hatrack representations in combinationwith our research of available mass-produced hatrack models in the historicalrecord (found in period catalogues, patents, museum collections anddesign books).

The 5 interactive hatracks are meant to offer spectators a shortcutand assistance in their efforts, not only to review my arguments butto allow them to experience, and to explore and build upon their ownanalysis to process, and later to generalize from the facts before us.

The order of occurrencesand the quantity and choice of 5 interactive models above differs fromthe earlier illustrations #2A, B, C, D, E, and F that I originally sitedas Duchamp’s 6 hatracks cuts. For clarity, I will discuss each of the5 interactive models separately starting with the 1904 Thonet catalogueimage and 3D model.

What To Look For:

1. 1904 Thonet Hatrack – Interactive Model

After examining Duchamp’s 6 hatrack representations, and after canvasingthe historical record, I concluded that; A. Six different 3D hatrackswere described by Duchamp’s 6 representations (five 2D, one 3D); B.No duplicate, mass produced, readymade store-bought hatrack matchedany of the five 2D representations or the one 3D Schwarz model. C. Theclosest possible mass-produced hatrack circa 1915 or before that I couldfind (after considering the varied deviations within the five 2D depictionsand the one 3D model), was the common Thonet bentwood hatrack (a designstill commonly found today in both metal and wood).

4 Hatracks from the Art Science Research Laboratory (ASRL) Collection
click each image to see video

• Illustration 7A
• Illustration 7B

• Thonet Hatrack, circa 1904
• Metal Hatrack, circa late 19th, early 20th

• Illustration 7C
• Illustration 7D

• Bentwood Hatrack, circa late 19th, early 20th century
• Thonet Bentwood Hatrack, circa late 19th century

See illustrationsand videos 7A, B, C, and D showing lab members hanging hats on fourhatracks from the Art Science Research Lab collection. The first woodmodel below is the closest one that we have found that has characteristicscommon to all six of Duchamp’s hatrack representations, and appearssimilar to Thonet bentwood style #11022. Thonet Brothers mass-manufacturedand shipped their original Bentwood designs throughout the world. Seeillustration #8A, B showing the title page for the 1904 catalogue andthe page for hatrack #11022. Trythe Thonet 1904 interactive 3D model. Note how symmetrical thehatrack appears and how it matches the catalogue drawing.

The patented technologythat allowed Thonet to permanently shape wood for furniture withoutcarving (hence bentwood), became immediately recognizable by the “S”curve module units. Note too, that the illustration 7A Thonet hatrackhas three “S” curves on a round base. The 7B and 7C Thonet-stylehatracks, one in metal and the other in wood, also have 3 “S”hooks. Click to see videos of each hatrack in the ASRL collection. Theillustration 7D video shows the official Thonet paper label on the back.As you can see from all 4 videos, each of the hatracks are wall units,and each can easily hang hats. BothThonet catalogue pages illustrations #9 and 8B show examples of thecommon bentwood hatrack/coatrack free-standing models still in use today.

click images to enlarge

• Illustration 8A
• Illustration 8A
• Illustration 9

• Frontispiece of “Thonet Bentwood
  & Other Furniture,”
  illustrated catalogue, 1904 New
  York: Dover Publication, 1980
• “Thonet Bentwood &
  Other Furniture,” illustrated
  catalogue, 1904, p. 80
  New York: Dover Publication, 1980
• “Thonet Bentwood &
  Other Furniture,” illustrated
  catalogue,” 1904, p. 81
  New York: Dover Publication, 1980

click to enlarge

Illustration 10
Wireframe of a computer
generated Hatrack based
upon 1917 studio photo

This studio photograph was reproduced as a retouched print in the 1941 Boîte en Valise. Count the hooks. There are 2 long hooks and 3 short hooks. We took the 3D model of the Thonet hatrack with the 3 “S” hooks, compared it to this studio photograph print and noted the differences. If the first long hook and short hook are, together, one “S” hook of the Thonet model (with a total of three “S”s), then the second long curve and short curve could together be the second “S”. But the second long hook (having a much more open and soft curved shape when compared with the first long hook’s curve) cannot be the same shape as the first long hook.

Rotate the 1917 (above the Thonet 1904) interactive hatrack 3D model away from the 2D photo underneath and compare the differences. Note that the 3D model’s second “S”‘s long curve is not open and soft like the second “S”‘s long curve in the photograph⁽⁸⁾. Yet, the second “S”‘s long curve in the 3D model approximately matches the first “S”s long curve in the photograph.

Moreover, the 2nd”S”‘s bottom, small hook is a wider shape and less curvedwhen compared with the first “S”‘s bottom small hook. Finally,the third small hook is missing the top, long hook part of the “S”.In order to represent Duchamp 1917 2D depiction in 3D, we had to cutoff the long curve from the “S” hook and leave the bottomsmall hook curve in yet a different angle from the first and second”S”‘s two bottom small hooks. See illustration #10 that showsa front view of this hatrack with its cut off long hook. Rotatethe interactive 1917 3D model into the face forward position (like theThonet 1904’s position) and then go back to compare the Thonet 19043D model. Importantly, try to place this Thonet 1904 into similar positionsas the first or second “S” hooks in the 1917 Duchamp 2D depiction.(The 3D Thonet model here is slightly squatter than Duchamp’s 1917 hatrack.)

3. 1917 Hatrack (3rd Interactive hatrack model from the bottom)

This studio photograph immediately appeared to be a more promising matchfor both the Thonet 1904 model and the 1918 shadow in the Tu m’ painting(see illustration 2A). However, all attempts to match a 3D model withthree identical and symmetrical “S” curves to the depictionthat Duchamp provides failed, asone can see by examining this 1917 Interactive 3D model. Again,return to the 1904 Thonet 3D model and try to place each of the model’sthree “S” hooks into similar positions as the 1917 hatrack”S” hooks found here. As observed in the previous 1917 photo(2nd hatrack from bottom), the Thonet 3D computer model has tightercurves and shorter hooks then in our actual wooden Thonet 3D model fromthe ASRL collection shown in #7A.

4. 1964 Blueprint with Interactive 3D model of lost version, Schwarz 3D Hatrack model

This blueprint turns out to be a poor interpretation made by an anonymousdraftsman while tracing the 1917 Boîte en Valise (see illustration11A, showing overlay of 1941 Boîte hatrack [placed on its side]with the blueprint. See the circled section on #11B and compare thisto the circled part of #11C, instead of interpreting the first smallhook (from the right) making a continuous “S” shapemoving from the first long hook on the right, the blueprint indicatesthat the 1st short hook is a separate piece awkwardly sticking out fromwithin the side of the first long hook. It is interesting to note thatthere is no indication of the draftsman having had a conception thatthe hatrack was made of “S” shapes anywhere in this muddleof 3 small and 2 long hooks, (with each hook having its own size andunrelated curved shape).

click images to enlarge

Illustration 11A
Overlay of the 1964 Hatrack blueprint with the 1941
Box in a Valise photograph (detail); individual images
shown on the right Note: circles are for clarity added by author

• Illustration 11C
• Illustration 11B

My examination ofother 1964 blueprints for other Schwarz readymades might be helpfulto mention here. Also signed “Marcel Duchamp, okay,” the bicyclestool blueprint is similarly ambiguously and inaccurately drawn (mostlikely because Schwartz’s draftsman did not know how to interpret thebroken legs and rails as depicted in the 1941 Boite-en-valiseprint of the bicycle wheel (also showing the coatrack). See illustration#12A, B and C, notice that the two most right horizontal rails in theblueprint go in two different directions and are cut off oddly, as depictedin the original studio photograph (12C). In addition, the 3 legs arenot evenly spaced as one would expect in a blueprint (and the fourthleg is missing completely) and yet in the final Schwarz edition (12D),all legs are completely symmetrical. Note that illustration 12B alsocontains the within 3D model we made using the information containedin the 1964 stool Blueprint (also 12B).

click images to enlarge

• Illustration 12A
• Illustration 12B

• Print made from of the
  original studio photo (1916-17)
  for the Box in
  a Valise, 1941
• Comparison of 1964 Blueprint
  of the Bicycle Wheel (Stool) with the
  ASRL 3D model made from its information

• Illustration 12C
• Illustration 12D

• Original Studio Photograph, 1916-17
• Bicycle Wheel, 1913/64,
  Schwarz edition of 8

The shovel blueprintindicates that the handle was literally traced from a well known ManRay photograph that captured the shovel hanging high above eye level,(see illustration 13A and B). At this height, as the eye looks up theshovel’s wooden shaft’s outside edges appear to converge (and get narrowerwith more distance.) To create a blueprint, perspective distortion mustbe accounted for (and discarded) if you use a photograph as a sourceto recreate an accurate 3D model. See the shovel blueprint illustration13B, the front and side elevation views both depict the converging linesthat were later, amusingly translated in the construction of Schwarz’s3D model. The shovel’s wood shaft, literally gets progressively morenarrow from metal blade to the handle. See illustration 13C showingthe final Schwarz 3D model built from the blueprint as a much smaller3D model on the left than the shovel on the right that was built frommeasurements of actual example of the Schwarz edition of 8 snow shovels)⁽⁹⁾.

click images to enlarge

• Illustration 13A
• Illustration 13B
• Illustration 13C

• Photograph of Duchamp’s Studio by Man Ray, 1920
• Marcel Duchamp, Blueprint for In Advance of the Broken Arm, 1964
• Front and side views of the ASRL 3D models of actual Schwarz shovel (left and longer) and a shovel made from the blueprint (the smaller one on the right)

Let us return to the hatrack blueprint 1964 and the 3D model. IfSchwarz’s 1st version of the hatrack 3D model, indeed, looked like thegeometry in this blueprint, it’s no wonder why Duchamp insisted uponthrowing it out and felt he had to redesign it.. . and yet his 2nd andfinal version of the Schwarz hatrack looks even less like the photographsof the “original” 1916-17 hatrack in his studio! (I will laterdiscuss the likely reason why Duchamp approached his hatrack in thistechnique of “information” that decays in a series of snapshotsover time).

5. 1964 Blueprint with Interactive version of 3D Schwarz model

click to enlarge

Illustration 14A
Marcel Duchamp, Hatrack, 1917/64

Before considering the interactive 3D model, one can see that the blueprint has nothing to do with what ends up as the 2nd and final version of the Schwarz 3D hatrack model. See video and illustration 14A of the Schwarz 3D model, in addition to the interactive model, how do we install this hatrack? Does it go on a wall? If so, how? If you place the 3 hooks up, the other 3 hooks go down, and half are therefore useless. Placing 3 on the left side and 3 on the right side is not much better. Sitting on a table does not make sense; neither does somehow hanging it upside down from the ceiling. The radial, symmetrically distributed series of curves definitely reminds one of the top the free standing-type Thonet coatrack/hatrack shown in illustration 14B and video 14E. However, as much as we are vaguely reminded of such a hatrack, a critical comparison quickly reveals that the tops of these Thonet free standing structures are a circular series of “S” curves. Moreover, Schwarz’s hatracks (edition of 8) are not even bentwood but have been carved as shown earlier in illustration 14C and D (our study model of the Schwarz editions). Moreover, note that the 6 equal length hooks curve out whereas the real free standing Thonet “S” hooks at the top curve in⁽¹⁰⁾, see illustrations 14 C and D. 14C reminds us of the top part of the “S‘s” in the standing Thonet (14B); whereas, 14D reminds us of the S‘s lower set of curves that turn up.

click images to enlarge

• Illustration 14B
• Illustration 14C, 14D
• Illustration 14E

• Thonet standing hatrack, “
  Thonet Bentwood & Other Furniture,”
  illustrated catalogue, 1904, p. 80
• ASRL wood model of Schwarz 1964
  Hatrack wood 3D model in two positions
• 1999 version of ‘Alice in Wonderland’
  uses Thonet hatrack as prop ©
  1999 Babelsberg International Film
  produktion GmbH & Co. Betriebs
  KG and Hallmark Entertainment Distribution Company

Compare5 Interactive Models with Tu m’ and Cast Shadows Depictions

click to enlarge

Illustration 15A
Marcel Duchamp, Tu m’
(detail; rotated by 180º), 1918

Illustration 15B
Historical Thonet hatrack, 1904

The final 2 representations from Duchamp’s 6 depictions thatwe will discuss are Tu m’s 1918 hatrack and Cast Shadows‘hatrack, 1918. These are both shadow projections that can also be comparedto five interactive 3D models (1904, 1917, 1917, 1964, 1964)

The Tu m’ shadow’s2 long hooks and 3 short hooks, in particular, (see illustration 15A,B) if viewed upside down and then compared to the 1904 Thonet modelwhen rotated into similar position, can readily be seen as fragmentsof 3 “S” shape hooks (albeit, that the 3 “S”‘s inTu m’ are incorrectly and asymmetrically angled in relation toeach other and the top of one is cut off when compared to the Thonet1904 3D model below).

The 1918 Tu m’ painting brings us back to the issue, previouslymentioned, of the difference in making objects in 3D, versus interpretingwhat these same objects look like, due to distortions, in a photograph,or in perspective drawings. Just as a bicycle wheel can objectivelybe perfectly round in shape and yet appear in a photograph as an ellipse,the same is true of any object’s representation. Representations mustbe interpreted. We, in fact, because of a prior experience, can safelyguess that the bicycle wheel is round but only appears to be an ellipsedue to perspective distortions. However, an alternative hypothesis couldbe true, though not as likely — that the bicycle wheel is not roundbut shaped like an oval. How can we know? The answer is two-fold. Ifwe have access to the original wheel, we can test it (roll it and seeif it smoothly and evenly rolls) and measure it (and see if the axisis in the middle of the circumference of a circle).

In the case of Duchamp’shatracks and other readymade objects, we are in the same position ofdiscovering that a bicycle wheel that we assumed was round in a photographwas, in fact, oval. Since we only had a set of photographs of the secondversion of the Bicycle Wheel, and not the actual object, theonly thing we could do was to take measurements from the 2D representations,fuse and build 3D models (both physically and in computers) based uponthe group of photographs, and then test and measure again.

Click for video

Illustration 16B
Assembled 3D model of Bicycle
Wheel by Rhonda Roland Shearer

Ironically, my bicycle wheel example turns out not to be hypothetical. Seeillustration 16A, B. From the set of bicycle wheel photographs, afterwe made measurements and models, and tested them, Robert Slawinksi, inour ASRL group, concluded that the axis of the Duchamp bicycle wheel was,in fact, not in the center of the wheel! Duchamp had lengthened some spokesand shortened others to create a large and surprising effect that is basedupon only a very small difference in the decentered positioning of theaxis. Click on #16B to see the video of what happens when our 3D modelof one of Duchamp’s bicycle wheels turns⁽¹¹⁾.

click images to enlarge

Illustration 16A
Setof photographs showing the 2nd version of the Bicycle Wheel,1916-17
(Both the original and this 2nd version are lost.There are no representations knownof the 1913 original Bicycle Wheel and Stool.)

click to enlarge

Illustration 17
Marcel Duchamp,Ombres Portées
(Cast Shadows), 1918
Note: arrow is for clarity
added by author

The Cast Shadows 1918 photograph shouldalso be examined by spectators in comparison with the 5 interactive hatrackmodels, see illustration 17. This representation of the hatrackindicates 3 long hooks and two short hooks. The first long hook on theleft, hanging by a string, ambiguously appears as if it could be attachedin a whole “S” shape with the first small hook on the left. A more likelyinterpretation is that the middle long hook is one “S” curve with thefirst (left) small hook and that the long hook at the most right is connectedto the right most small hook. Yet this is unclear for the right most longhook could share an “S” shape with the left most small hook. In additionto the hatrack shadow ambiguities, other ambiguities reign in this photograph.For example, Duchamp’s work Hidden Noise (see illustration 18A,a closeup of the Cast Shadows, 1918) oddly appears twice(he supposedly only had one original in 1918 — the multiple edition of8 was made much later in 1964, see #18B that shows the original HiddenNoise.) One has to conclude that Duchamp either somehow used mirrorsto multiply the Hidden Noise shadow, or he created a photographiccomposite where he layered different photographs together into one image⁽¹²⁾.Duchamp used both techniques in his photographs, a topic we will explorein the next section.

click images to enlarge

• Illustration 18A
• Illustration 18B

• Ombres portées
  (Cast Shadows), detail
  showing two shadows projecting from
  With Hidden Noise (1916),
  1918 Note: circles are for clarity added by author
• Marcel Duchamp, With
  Hidden Noise with
  mirror, 1916

Duchamp’s readymade hatrack only
exists in the mind not in factual nature.

Afterduly noting the geometric distortions in Duchamp’s six hatrack representations,we must conclude that the simple history and definition of the hatrackthat everyone believed — that a readymade is an unaltered, mass-producedobject — must be completely reassessed and rewritten.

We can return to the six representations of the hatrack and explore some of the issues now raised such as to how Duchamp generated the six depictions? Did he alter hatrack objects or doctor photographs or both? We are presently working with forensic scientists to help us determine more about the exact nature and type of photographic or physical manipulations that Duchamp may have used. Duchamp, obviously, put us all on notice that he was doing the photographic tricks well known in the late 19th and early 20th century by both amateur and professional photographers, see illustrations #19A, B. In both photographs 19A and B, Duchamp himself appears to be a ghostly apparition, a typical photo trick of the time.⁽¹³⁾

click images to enlarge

• Illustration 19A
• Illustration 19B

• Studio photograph(1916-17) with
  Duchamp’s ghost image found in 1960’s
• Photographof Duchamp’s studio
  by Man Ray with Duchamp
  as ghost image, 1920

Illustration 20A
Original Studio Photograph, 1916-17

Forensic experts thatI have consulted also noted that the scale, shadows and light directionsin many of Duchamp’s photographs are inconsistent throughout the wholeimage.⁽¹⁴⁾As an example, strong shadows will, inconsistently, be cast from oneobject but not from the other object directly next to it. (Closely examineillustration 20A, Note that the stick leaning against the wall casta shadow and yet the Bicycle Wheel does not! Moreover, the pillowsin the foreground cast strong shadows and yet the Coatrack doesnot!)

For another example, look at illustration20A, B and C. A full size snow shovel could not possibly be hanging physicallyfrom a height indicated in these studio photographs. We discover thatthe wood shaft would have to be too short when we compare the shovel’ssize to the ceiling.

click images to enlarge

• Illustration 20B
• Illustration 20C

• Photograph of Duchamp’s studio used
  for making print for the Box in a
  Valise, 1941Note: circle is for
  clarity added by author
• Notethat shovel could not be hanging
  at its full length from the ceiling.
  Photograph of Duchamp’s studio with
  Duchamp’s ghost image, 1916-1917
  Note: circle is for clarity added by author

click to see video

Illustration 21A.
Marcel Duchamp, In
the Manner of Delvaux, 1942
Note: arrows are for clarity
added by author

Illustration 21B
Mathew Brady used composite
techniques in the earlist
days of photography.
From Dino A. Brugioni, Photo Fakery:
The History and Techniques
of Photographic Deception and
Manipulation, Virginia: Brassey’s,
1999, p. 34
Note: circles are for clarity
added by author

Our resulting hypothesismust be that the shovel’s wood shaft and handle have been somehow cutoff. Duchamp (or someone in his behalf) shortened the wood shaft eitherphysically or photographically. In the later case of trick photography,instead of hanging a short snow shovel in his studio, Duchamp, or someoneat his behest, could have; 1); taken a photograph of a snow shovel andcarefully trimmed away the background; 2), Next, this snow shovel shapedphotograph part (with short wood shaft) would then be inset into a preciselysized and shaped cut out receptacle in the studio photo’s emulsion (similar to putting acut out cookie back into its negative space within the rolled out dough);3), the studio background and shovel fragment now appear as one photographthat is rephotographed and printed for the final resulting composite thatwe see. Examinehere the video of the work, In the Manner of Delvaux (1942) whichdocuments only one example among many of the expert skill Duchamp (orsomeone at his request) demonstrated in creating photographic composites.(See Illustration 21A) Adding or subtracking subjects from photos wasdone with numerous techniques from the earliest days of photography. MathewBrady seamlessly added an eighth Civil War general in illustration 21B.

The aforementionedstudio photographs (19A, B and 20A, B) present many other instancesof photographic manipulations that I will leave for future discussions.However, please see Stephen Jay Gould’s text box here to read his observationsand discovery regarding Duchamp’s studio photograph, illustration 19B.For now, I will limit myself to analysis of two studio photographs ofreadymades to continue my argument (see illustrations 22A and 22B thatshow Duchamp’s “original” 1916 coatrack and “original” 1917urinal.)

click images to enlarge

• Illustration 22A
• Illustration 22B

• Marcel Duchamp,
  Trébuchet, 1917
• Marcel Duchamp,Fountain,
  photograph by Alfred stieglitz
  from BlindmanNo. 2, 1917

One, might think at this point, “So what. I can alreadysee that Duchamp probably altered, physically or photographically, hisreadymade objects — what difference does this make?” Let’s set asidethe fact that all books of art history or cultural criticism (and evencookbooks! See illustration 22C) state, as their premise, that Duchamp’sreadymades are unaltered, store bought mass-produced objects – and thatthis claim can now be dismissed as factually incorrect.⁽¹⁵⁾I will use illustrations 22A and 22B to show that Duchamp’s original coatrackand urinal help explain why I believe Duchamp altered readymade objectsin his photographs in the first place. Since the quality and approachthat Duchamp used for his numerous distorted “readymade” representationsare similar, such a frequency of occurrence suggests that Duchamp wasapplying a single geometric system. Perhaps this system that I have beenobserving throughout Duchamp’s readymade works is the new and mathematicallyrigerous “rehabilitated perspective” geometry Duchamp spoke about in interviews.Moreover, I also found evidence that Duchamp used this new geometry inthe Large Glass, just as he had claimed.

click images to enlarge

• Illustration 22A
• Illustration 22B
• Illustration 22C

• Marcel Duchamp, Trébuchet, 1917
• Marcel Duchamp, Fountain, photograph by Alfred stieglitz fromBlindman No. 2, 1917
• Even a cookbook refers to Duchamp’s readymades as only humble, store-boughtobjects.
  David Rosengarten with Joel Dean and Giorgio DeLuca, THE DEAN & DELUCA COOKBOOK, New York: Random House, 1996, P. 206

In a 1966 interview with Pierre Cabanne, Duchamp states:⁽¹⁶⁾
Perspective was very important. The “Large Glass” constitutes a rehabilitation of perspective, which had then been completely ignored and disparaged. For me, perspective became absolutely scientific.

Cabanne:  It was no longer realistic perspective.
Duchamp:   No. It’s a mathematical, scientific perspective.
Cabanne:  Was it based on calculations?
Duchamp:  Yes, and on dimensions. These were the important elements. What I put inside was what, will you tell me? I was mixing story, anecdote (in the good sense of the word)⁽¹⁷⁾with visual representation, while giving less importance to visuality, to the visual element, than one generally gives in painting. Already I didn’t want to be preoccupied with visual language. . . .
Cabanne:   Retinal.
Duchamp:   Consequently, retinal. Everything was becoming conceptual, that is, it depended on things other than the retina.

Time Line of Readymade Series of “Trébuchet” Coatracks —
as Seen by Spectators

click each image to enlarge
23A	23B	23C	23D	23E
Click	Click	Click	Click	Click
1941	1960s (made 1916-17 found in 1960s)	1964	1983 (made in 1940 found in 1983)	1991 (made 1964 seen 1991)
Retouched 2D print in Boite-en-valise	2D photo original Coatrack	3D iron and wood model	2D print found by Ecke Bonk (made in 1940 by Duchamp for Boite)	2D Blueprint

Let’s look at the Coatrack (see illustration 23A, B, C, D, and E) as a series of snapshots in time, just as we did to examine Duchamp’s hatracks, as he instructed us to do in his notes (refer again to illustration #1).

Note that the geometriesof the coatrack series (as we also found in the hatrack series), isdifferent in every 2D and 3D representation. (For example, the ironhooks are straight in the 1964 Schwarz 3D model and 2D blueprint, whereasthey lean backwards in the original 1916-17 studio photograph and inthe 1941 Boîte print. And as in our treatment of the hatrackseries, we must mentally visualize or, alternatively, make literal 3Dmodels of the coatrack 2D representations, in order to observe the differencesamong all of the 5 coatrack representations (four 2D and one 3D).

The particular distortionscontained within the original studio photograph provide the greatestinterest for our immeditate discussion. Again, as we found in the hatrack,the coatrack hooks bend and turn in unanticipated ways. (We expect mass-producedobjects to have characteristics of the factory-made, traits that includestandardization and regularity of form — the very opposite of custom-madevariations). Look at the last hook of the 4 (moving from left most hookto right), the top small sub-hook (the middle of the three sub-hooks)bends so far up and in that it reaches the top largest sub-hook. Duchamptold us that he nailed the coatrack to the floor after having “kickedit around” his studio. However, this trauma to the coatrack (that heaptly titled “trap” or Trébuchet — a term from a move in chesswhere a player sacrifices one of his own pieces to trap an opponent’spiece) the physical properties of cast iron determine that such a hookwould crack and break before bending. This rigidity of material provesuseful for withstanding the stress of hanging heavy coats. Duchamp,on the 1964 blueprint, even specifies that his 3D 1964 Schwarz hooksmust be made of iron — not soft copper.

• 23FDuchamp’s distorted Coatrack
  in original studio
  photo, 1916-17
• 
• 

• 23G
  Actual historical coatrack
  in ASRL Collection with
  correct perspective
• 
• 

Illustration 23 F and G
Analysis done by Yong Duk Jhun and Rhonda Roland Shearer

click images to enlarge

• Illustration 23H
• Illustration 23I

• Method of identifying perspective
  distortion in a photograph —
  thus demonstrating evidence of
  photo manipulation — from Brugioni’s
  Photo Fakery
• Cover of Photo Fakery:
  The History and Techniques of
  Photographic Deception and Manipulation,
  by Dino A. Brugioni, Virginia:
  Brassey’s, 1999, p. 90

Note the shapes and count the holes in hook 24A and 24B and contrast these to the general form and number of holes found in Duchamp’s original Coatrack hooks in the studio photo and in the Schwarz model in 24C

In fact, when Robert Slawinski and I began working on creating a coatrack 3D computer model (equivalent to the information contained in the 1915-16 2D studio photograph) we quickly recognized that the hooks used by Duchamp were; a) a common type readily found in the historical record (see illustrations 24 A and B); b.) that his 3D Schwarz model of the coatrack looked nothing like the “original coatrack” found in the studio photograph of 1915-16 (for example, note that the hooks are straighter in the 3D model and that the wood board bottom extends too far past the hooks on each end in comparison to what we find in the original 1915-16 2D studio photograph, see illustration 24; c) not only is the last hook (moving from right to left) distorted in the original studio photo above (in 24C) (its top small sub-hook with an impossible upward curve), but the other 3 main hooks of the four, and the wood board itself, are also distorted. In other words, we cannot take the matching historical hooks (as in illustration 24B), place them evenly on a symmetrically rectangular wood board and then find one single perspective viewpoint to make a projection that matches all the shapes of the coatrack, as Duchamp has depicted them in the original studio photograph (see illustration 23A).

click images to enlarge

• Illustration 24A
• Illustration 24B
• Illustration 24C

• Historical coathook in the
  ASRL Collection that matches
  the one Duchamp used in original
  1916-17 studio photo
• Historical coatrack in the ASRL Collection
• Comparison of Schwarz 3D model’s
  wood base (bottom) and wood base
  as depictedin 1916-1917 original
  studio photograph (top)
  Note: circles are for clarity added by author

click to enlarge

Illustration 23E
2D working print
found by Ecke Bonk
that Duchamp made
in 1940 in the process of creating
a pochoir print for his1941
Boite-en-valise

See illustration 25 showing how the cube’s shape changes according to the position of theviewer’s eye position. When we know the original shape — such as acube or a series of identical coat hooks in a row — we can then accuratelypredict what the shape of the cube or coat hooks will be from variousobserver’s eye positions. In other words, if the resulting cube or coatrackshapes follow our predictions (based upon both our prior experienceand perspective rules), then we say that the representation is “correct”(in perspective geometry); if the cube and coathook shapes are not inaccordance with our predictions, then we say that the representationis distorted. As in our previous hatrack series, our two hypotheses are possible: first, that Duchamp altered the coatrack physically; or second, that he altered it photographically. The last image in the coatrack series of snapshots reveals, I believe, the photo composite technique that Duchamp used to make his coatrack and other “readymades” as well as disclosing the underpinnings and general methodology of his new form of perspective geometry. (see illustration 23E)

Illustration 25A depictsthe perspective found in photography — one fixed eye sees a continuousand related set of distortions from the perspective of this one eye.(The four different cube descriptions in 25A are what the eye sees from4 different fixed positions). Illustration 25B, however, more accuratelydepicts how we actually see objects, as our two eyes, head and bodiesmust continually move around 3D objects to fully see their forms, asshown with this cube. And yet, despite what must be the truly fragmentednature of the visual input, the mind and eyes work seamlessly togetherto create the appearance of discrete and fixed objects.

The two cube examples(25A and B) directly relate to the earlier discussion of Duchamp’s WhiteBox note, which, as I argued, describes 2 mental operations (seeillustration 26A and B). The single fixed eye perspective of 26A islike the fixed eye looking at the cube in 25A; whereas the moving eyeof 26B operates like the multiple perspectives described in 25B.

The notable difference between illustrations 25A,B and 26 A,B is the dimension. Using Duchamp’s terminology, 25A,B describes an eye in 3D space (“eye³“) looking at a 3D cube; whereas, 26A,B represents an eye in 3D space making observations of a 2D plane. Both 25B and 26B require time and movement in 3D space of the 3D eye ; whereas, 25A and 26A illustrate what Duchamp describes as the “vision” of the “same eye from a fixed point of view (linear perspective).”1

click images to enlarge

• Illustration 25A
• Illustration 25B

• A set of continuous and related
  3D cube distortions as seen
  from four fixed eye positions
• 3D cube is only seen as a
  3D eye moves around it

• Illustration 26A
• Illustration 26B

• Duchamp’s diagram 26A
  illustrates what is seen
  from a single fixed eye
  as in 25A above
• Duchamp’s diagram 26B illustrates
  more accurately how an eye moves
  in time and space to collect
  information as also shown in 25B above

click to view

Illustration 27
Video of Coatrack
animation analysis

In order to actuallysee all of the coatrack information seen in Duchamp’s original studiophotograph in real 3D space, our eye would need to be moving in time– see Illustration 27 showing a video of Robert Slawinski and my animation.Our analysis of the original coatrack depiction reveals that Duchampused a common composite photo trick to “cut and paste” togetherhis “whole” coatrack. Using 6 different photographs from 6different fixed eye viewpoints, we believe that Duchamp cut out onesection of the coatrack from each photo and then carefully fused theseparts together for the final appearance of only one readymade coatrack.The spectator would only “see” this actuality of multiplepoints of sight “non-retinally,” with conscious effort viamental visualization or actual model-making.

We made both physicaland computer models here in the lab. Our computer animation diagramsthe 6 cuts we believe that Duchamp made from 6 separate photographstaken in 6 different perspective positions. Robert Slawinski and myanalysis concludes that Duchamp used 3 whole hooks, 1 hook split into2 parts and 1 whole wood board as the 6 parts (from 6 different photos)as he assembled into what appears to be the single, whole and readymadecoatrack in his studio photograph. See Illustrations 28A, B, C, D, E,F, the 6 coatrack parts that Duchamp cut out and later assembled togetherare color coded (in these still images taken from the computer animation)to emphasize the separation of the part selected by Duchamp from therest of the coatrack (that he then discards, and that follows the sameperspective geometry of the targeted part.)

click images to enlarge

• 28A
• 28B
• 28C

• 28D
• 28E
• 28F

This series of stills shows each of the 6 coatrack positions
from which Duchamp selected parts to composite
(Note: The selected parts are color-coded)

Illustration 29A and B show a comparison of the parts that Duchamp selected (in color coding) with an image that assembles the 6 whole coatracks, in their 6 different perspectives, together into one event simultaneously seen (using the same color coding).

click images to enlarge

• Illustration 29A
• Illustration 29B

• A color-coded diagram
  showing the 6 parts Duchamp
  composited together taken from 6 photos.
• This still from our coatracks
  from which Duchamp selected
  parts to composite (as in 29A).

click to enlarge

Illustration 30
A photo trick book points to
the problem of “fluffy contours”
created by the unintentionally
cut and paste method, revealing
that photo compositing has been made.

Illustration 31A

Illustration 31B
Here are two pages from a
photo trick book discussion
about the “cut and
paste” method used for
creating photo composites.

In addition to the evidence resulting from our analysis of the perspective geometries,2 other examples of internal evidence indicate that Duchamp used both”masking” and “cut and paste” techniques from thephoto alterations used in hobby and trade.

Examine illustration30, a close up view of Duchamp’s original coatrack photo, revealingwhat a photo trick book calls the “fluffy edges” that caneasily appear as a soft whitish outline around a photo cut-out afterbeing pasted, if special measures are not taken. Forensic experts lookfor tell-tale signs — such as fuzzy contours– as indicators that photo prints have been combined. See illustration31A and B,two pages from “The Secrets of Trick Photography”by O.R. Croy discussing this particular problem within the cut and pastemethod.

Our second exampleof internal evidence for our hypothesis that Duchamp altered his originalcoatrack photograph by combining parts returns us to illustration 23E.Only after making our animation analysis of the geometries in the coatrackdid I notice the potential importance of Duchamp’s “working”prints of the coatrack first published in 1983 by Ecke Bonk. These printswere described by Bonk as preliminary stages of Duchamp’s 1940 processin preparing pochoir prints for his publication of 300 copies of theBoîte-en-valise, (see illustration 32A and B). Bonk doesnot explain what the method was, or why Duchamp was cutting and pastinga separate paper cutout of the coatrack onto the background studio photo(where 3 hooks are masked out of the scene with white). Illustration32B indicates an attempt to position only the first hook of the cutoutonto the coatrack underneath. This “working print” also suggests(as judged by their two positions) that the paper cut-out coatrack isin one perspective view and the coatrack underneath, imbedded into thestudio photo background, is in another perspective.

Compare this working print (32B) to our still from the video animation, where we concluded that Duchamp used 6 different viewpoints (cutouts of hooks and a wood board from 6 photographs), see illustration 32C. The similarity between 32B and C is striking. Was Duchamp using the same method of compositing multiple viewpoints into one coatrack for his pochoir print that he had used earlier to create his original coatrack in the studio photograph?

click images to enlarge

• Illustration 32A
• Illustration 32B
• Illustration 32C

• Marcel Duchamp, Boite-Series F, 1966
• Working print used by
  Duchamp to create his 1941
  pochoir print for the Boite-en-valise
• A still from our coatrack
  analysis that appears strikingly
  similar to Duchamp’s working print above

I believe that this working print serves as a “smoking gun” in our case. Not only is the cut and paste method and the geometries of the forms similar between the alterations in the studio photograph and in Duchamp’s Boîte pochoir print, but his separate white-out and maskings of the wood board and the hooks now makes sense. For what purpose would the separate masking and treatment of the 4 hooks and the wood base serve (as is clearly indicated in his “working print”) other than as a matrix for creating a composite image?

click to enlarge

Illustration 33A
Known stieglitz version of
Duchamp’s Fountain
urinal publishedin
Blindman N. 2,1917

Illustration 33B
Second version of stieglitz’s
Fountain photo (1917)
not publiclyknown until 1989

Related to evidence of photo compositing, as found within Duchamp’s “working print”of the coatrack, is a curious 2nd version of a photograph of Duchamp’sFountain urinal taken by stieglitz in 1917, and shown in illustration33A and B. William Camfield’s 1989 book, a chronicle of the odd historyof Duchamp’s Fountain urinal, presented this second stieglitzphoto for the first time after it quietly appeared within the archiveof Duchamp’s main patrons, the Arensberg’s, in the 1950’s.

Before discussing the potential importance of this particular photograph, and its delayedappearance for spectators, let us again examine, as we did with thehatrack and coatrack, the consistent approach that Duchamp uses to presenthis readymades — as a series of snapshots over time — now appliedto Duchamp’s urinal.
As we discovered with his snow shovel, hatrack, coatrack, bicycle wheeland stool, Duchamp’s original 1917 urinal does not exist today. Historianssuch as William Camfield and Michael Betancourt have documented thecontradictions and conflicting stories that leave us with effectivelyno definitive evidence about the urinal’s existence — including anypotential witnesses of the object (the few testimonies that exist conflict);who photographed it (stieglitz himself, who supposedly photographedthe urinal for the 1917 Blindman publication, only briefly mentionsthe urinal in writing, and no negative or print was ever found in hisarchive); or how it quickly the urinal vanished into thin air in 1917.I will not go into the details here, for they are so well pursued anddocumented by Camfield and Betancourt. All that we do have, as for Duchamp’shatrack, coatrack, and other readymades, is a series of urinal representationsin 2D and 3D that we can put together in a set (as in step A of Duchamp’smental operation). We can then examine each depiction as its own snapshotor cut (as in Duchamp’s step B, where we take separate observationsover time). Since the original 3D urinal is “lost” as a sourcefor collecting more information, we must depend upon our ability toaverage among, and compare differences between, each urinal representation,see illustrations 34A, B , C, D, E, F, G and H. The tally of our representations,encompassing what we know of Duchamp’s urinal, follows:

Time Line of Readymade Series of Urinals — As Seen by Spectators (click each image to enlarge)
34A	34B	34C	34D	34E	34F	34G	34H
1917	1941	1941	1960s (made 1916-17 found in 1960s)	1964	1964	1964	1989 (found 1950s published 1989)
2D photo by stieglitz from Blindman #2 journal, 1917	3D miniature model in Boite-en -valise	2D print made from studio photo in Boite-en valise	2D photo, studio photo	2D etching, edition of 100	3D pottery model Schwarz edition of 8, second corrected version by Duchamp	2D set of blueprints (first 3D model, based upon blueprints, lost)	2D photo fragment published by William Camfield (original dating not known)
Note: This time line excludes urinal versions that Duchamp did not originate.

As we discovered when examining Duchamp’s hatrack and coatrack, the above set of urinal depictionsin 2D and 3D do not describe one consistent 3D urinal. For example,our analysis of the studio photo 1916-17 (illustration 34D found inthe 1960’s), the 1941 print (illustration 34C created from a 1916-17photograph) and the 1^st version of the stieglitz photograph(illustration 34A published in the Blindman #2) reveals an inescapableconclusion — namely, that two different urinals were represented in1917. Again, our key question involves casualty — did Duchamp change urinals literally or photographically? Evidence for both hypothesesexists. Duchamp did make his original 3D miniature urinal model in 1940,and he did commission others to manufacture the full edition of 300.Surprisingly, after Duchamp authorized Schwarz to make editions of 14of his “readymades,” Schwarz failed, despite intensive search,to find even one of the 14 mass produced objects close enoughto Duchamp’s originals in 2D or 3D to serve as prototypes for the editions.Therefore, Schwarz had to organize the manufacture of all 14 editions himself. Stranger still, no duplicate urinal has even been found inany catalogue, including the literature from the very company that Duchampspecifically named his source for his urinal — the Mott company.

One of the nice twists of history’s perversity is that, while theDuchamp Fountain exists in numerous replica versions, asurviving example of the original type of urinal has proven impossibleto locate. If it exists at all, it is now an item of exquisiterarity.
Kirk Varnedoe, Adam Gopnik,
High and Low: Modern Art and Popular Culture, MOMA Catalogue,1990

click to enlarge

Illustration 35A
Urinals were purchased by Mott,
Crane and other plumbing companies
from Trenton Potteries in Trenton, NJ.
The Bedfordshire urinals in the ASRL
collection are all stamped Trenton potteries.

Art historians WilliamCamfield and Kirk Varnedoe report that they strenuously searched thehistorical record for urinal models that matched the geometry of Duchamp’surinal. My own research agrees with their conclusion — that the closesturinal to Duchamp’s is a model called the “Panama” or “Bedfordshirewith Lip.” In the early 20^th century, Mott, Crane andother distributers purchased urinals from Trenton Potteries, Trenton,NJ (a.k.a. “the sanitary pottery capital of the U.S.”). Modelsof urinals and other pottery products, such as toilets, were so basicand so infrequently changed that only freelance workers were neededto serve as modelers for the entire sanitary pottery industry. ASRLowns three of the Bedfordshire urinals, and all are stamped, “TrentonPotteries,” NJ; see illustration 35A. The duplication of shapeamong these urinals speaks both to the minimal variation that occursamong urinals, and to the easy standardization of form resulting fromtheir mold making process.

Just as one hatrackstudio photo, found in the 1960’s, provided a closer match (but no cigar)to the Thonet historical model than any of Duchamp’s other 2D or 3Dhatrack depictions, his urinal in two studio representations (34C and34D) provide a close, but not exact, match to the Mott historical model(see illustration 35B,C and D,E). Duchamp’s two studio photo urinalsare here compared to the Bedfordshire urinal with lip from the ASRLcollection, placed in a similar position. The general appearance issimilar among 35B,C and D,E. However, the “side ear-like”brackets are larger and different, both from each other and from theMott model, as are the pipe connections at the urinals’ top and bottom.Moreover, we have concluded from our analysis that one should be ableto see Duchamp’s “R. Mutt 1917” signature and date (and one cannot)on a urinal when placed in both positions 35B and 35C, if the inscriptionwere indeed there.

click images to enlarge

• 35B
• 35C

2 studio photos (35B, C) look similar
to the Mott/Crane Bedfordshire
with lip in 35D,E below;
Compare with detail images below

click images to enlarge

• 35B detail
• 35C detail
• 35D

• The 35B position would show
  the signature “R. Mutt
  1917″if it were there
  in the above studio photo
  — as indicated byour 3D
  computer model when placed
  in a similar angle.
• The 35C position would show
  the “R. Mutt 1917”
  inscriptionif it were there
  in the above studio photograph
  — as indicatedby our 3D
  computer model placed in a similar angle.
• 35E
  ASRLBedfordshire urinals placed
  in similar positions to urinals
  inDuchamp’s studio photos look
  easily similar, see 35B, 35C

However, when we examine35B,C,D,E various attempts to place the Bedfordshire model in a positionto match the stieglitz photo 36A completely fail. Only when we compositetogether the top part of the urinal from one photograph, the bottompart from another and the drain holes and pipe hole from yet othersin different perspectives, does the urinal begin to look vaguelylike the stieglitz urinal 36A. Note that the bottom and top of the urinalsin 35B,C and 35D,E easily appear similar in size, scale and perspectiveview, whereas, in 36A, the stieglitz original photograph appears tobe in one perspective view in the top half and in yet another cameraviewpoint in the bottom half where the pipe connection rests. Moreover,when you look at our actual Urinal, 36D for example, the upper halfwith the drain holes looks further away from us in the photo; whereas,the bottom pipe hole part appears closer to us, in the foreground. Curiously,no similar “near and far” positions are transmitted by theforms in 36A, Duchamp’s 1917 stieglitz photograph. In fact,in our Bedfordshireurinal photos, 36B,C,D,E, the drain holes appear smaller, and thereforefurther away, and the pipe hole reads larger and therefore closer tous than in the 36A stieglitz photograph — giving credence to my observationthat the stieglitz photograph, strangely, does not depict the significantdistance between the back of the urinal and the front (as clearly indicatedin 36B).

Click each image to enlarge     36A 36B Theoriginal stieglitz 1917 photo of Duchamp’s urinal, unlikeDuchamp’s two other studio photos, could not be easily approximatedwhen we photographed our Bedfordshire urinals. The Bedfordshireis the only urinal model, circa 1917, that appears closeto, but not identical to, the original urinal depicted inthe stieglitz photo. 36 B,C,D,E are a series of photographs of our ASRL Bedfordshire models that show our attempts to reproduce a shape similar to the urinal in the original 1917 stieglitz photo. 36C 36D 36E

Click to enlarge

Illustration 37A,B,C,D

We combined four different photographs to create 37A,B,C,D — asour Bedfordshire urinal’s drain holes, pipe hole, urinal top andbottom parts could not be captured in one photograph with positionsthat match the drain holes, pipe hole, and top and bottom parts in the stieglitz photo (36A).

We provide the 2D Interactive Presentation below to allow the spectator to experimentwith the cutting up and pasting together of different urinal photo parts.There are 9 possible combinations. One combination matches the stieglitzphoto. Also, try placing the pipe in the middle as we suggest. One canbegin to see how pieces that do not originally go together can be movedand will there appear to be better, or at least, equally correct intheir form, when in a new position — especially if you had the abilityto fill in gaps with even more cut-out parts then we provide in thispresentation.

		click here for 2D Interactive Presentation
		To download Flash Player plug-in, click here
Partialstieglitz photo found in 1980s is combined with part cut fromstieglitz 1917 photo (see part below)
This bottom part is cut from the original stieglitz photo, 1917

click to enlarge

Illustration 38A
In 1917, Duchamp places,
what I believe to be,
a composited photograph,
in a journal titled
The Blind Man

Illustration 38B
The Blind Man No. 2: P.B.T., May 1917

More specifically, this Interactive Presentation places together the bottom part, cut fromthe entire Stieglitz original photograph (36A), with the mysteriouspartial version (also printed from an original negative) as the top.Perhaps, as in our coatrack example, where the working print probablyrevealed Duchamp’s methodology for compositing his coatrack togetherfrom a series of photos in different perspectives, perhaps this partialphoto of the urinal, printed and left as a complete image, representsthe smoking gun, also found to reveal similar evidence of being a photocomposite. For if we can, (1), easily create a likeness of the two 1917photos of Duchamp urinals using the Bedfordshire 3D models and yet,(2), run into difficulty when doing the same experiment by trying torecreate the 1917 Stieglitz original urinal photo with the same Bedfordshire3D model (the main difference being that the top part of the urinal,as in the partial Stieglitz photo, lies in one perspective and the bottompart in another), then perhaps the partial photo discloses itself asa step that Duchamp used in a process of creating his final photo composite,then aptly published in The Blind Man as he realized that wewould not readily see his alterations. (see illustrations 38A and B.)

click to enlarge

Illustration 39A
Is the Partial Stieglitz
photo itself a photo
composite?

Is this partial Stieglitz photo itself, that we see in illustration 39A, also made of parts? Andis the complete version of the Stieglitz photo (38A) essentially a fusionof yet more parts added to parts already composited in the top photoof the partial version (39A)? Moreover, is the fusing of different perspectivespassing as one perspective in Duchamp’s urinal, hatrack and coatrack,the same “rehabilitated perspective” geometry that he claimsto have been using in his Large Glass?

Beyond “cut and paste” — what other photo tricks did Duchamp use?

As previously described,I had suspected that the Stieglitz partial urinal photo representeda step in Duchamp’s photo compositing process, and that this photographicpart, was itself, perhaps, made of photo parts. Illustration 40B suggeststhat, indeed, the drain holes were added within the Stieglitz partialphoto, which, as a subtle but visible vestige, remains in the originalStieglitz photo, see illustration 40A.

Note that in illustration 40B, when the contrast of light and shadow are amplified, the drainholes reveal a distinct boundary that is, unexpectedly, and withoutapparent reason, lighter in value, thus giving the literal appearanceof having been added as a patch.

click images to enlarge

• Illustration 40A
• Illustration 40B
• Illustration 40C

• Known Stieglitz version
  of Duchamp’s Fountain
  urinal published in
  Blindman No. 2,1917
• When the contrast of light and
  shadow are amplified, the drain
  holes reveal a distinct boundary
  that is, unexpectedly, and without
  apparent reason, lighter in
  value and gives the literal
  appearance of having been
  added as a patch.
• Examine the circled area in
  illustration 40C. The indefinite
  shadows and discontinuous lines
  and edges indicate this lower
  left corner as a likely site of
  photographic compositing and retouching.

The urinal in the Stieglitz photo, shown close up and large, created a greater technicalchallenge for hiding alterations than in our previous examples of thehatrack or coatrack, that are depicted as farther away and small, andtherefore creating less expectation of perceiving visible detail. Sincehatracks and coatracks are, literally, made of parts (the hooks andwood base are all physical parts put together), photographic cuttingand pasting of parts can naturally exploit these predetermined and expectedjoinings, whereas, the urinal’s smooth and continuous, singular formdoes not offer such easy opportunities.

Illustration 40C depicts yet another important piece among numerous pieces of evidence (pun intended).Porcelain urinals are molded forms that produce clean, clearly unambiguouslines and edges as shown in illustration 40D, E, F, (depictions of Bedfordshiretype urinals taken from Mott, Crane and Trenton Potteries cataloguesof the period [circa 1917]). Examine the circled area in illustration40C. The indefinite shadows and discontinuous lines and edges suggestthis lower left corner as a likely site of photographic compositingand retouching.

click images to enlarge

• Illustration 40D
• Illustration 40E
• Illustration 40F

• Trenton Potteries
• Mott
• Crane

Three different company catalogue entries (circa 1917) featuring the same urinal type that looks most like Duchamp’s urinal

We are presently working, along with forensic experts, on a substantial list of other odditiesfound within the Stieglitz photo (40A) including: (1), more precisedetermination of the nature of the distortions, first noted by WilliamCamfield, between the urinal in the foreground as depicted in relationto the painting in the background. We will also analyze and try to relatethe seemingly strange scale differences among objects in the Stieglitzphoto; such as the size of the urinal itself in comparison to the gaugeof the string tied to the left “ear-bracket”; or the relativelytoo large appearance of the rough hewn texture of the wood pedestal;(2), testing the feasibility of placing the urinal (whose actual form,not shown, is hollowed out underneath) so off center on the pedestal,as depicted on the photo; and (3), studying the strange shadows, lighting,as well as the peculiar reflections (reminiscent of pooling urine),in the top upper lip of the urinal — a pooling that appears to be defyinggravity. (If these reflections were actually urine, we would have tobe standing above, strattling a normally installed urinal in a novelorientation — with our backs against the wall looking down into thepool of urine and facing out to whoever would be peeing.)

A second compositingmethod, beyond cut and paste, is suggested within the two studio photodepictions of Duchamp’s urinal, see illustrations 41A, B, C, D. A commonbut more difficult method of combining photo parts uses a dark or blackbackground (cardboard or cloth) placed into a scene with a correspondingspace left blank on the photographic plate in the camera. In this blankspace, a second image (not in the immediate scene) can then be seamlesslyadded into both the plate, and also into the (formerly) plain blackbackground.

click images to enlarge

• Illustration 41A
• Illustration 41B

Two Photographs of Duchamp’s studio taken in 1916-17
A common but more difficult method of combining photo parts depends upon the use of a dark or black background (cardboard or cloth) placed into a scene and a corresponding space left blank on the photographic plate in the camera
click images to enlarge

• Illustration 41C
• Illustration 41D

Close-upviews of the Duchamp’s studio photographs (41A and 41B) Carefullynote the general blackened area behind the urinal in illustration41B and 41D and the dark cloth hanging directly behind the urinalin illustration 41A and 41C.

Illustrations 42A, B, C, D show a few early examples from a 1898 book written for the general public, and titled, Magic; Stage Illusions, Special Effects and Trick Photography. Compare these four illustrations to illustrations 41 A, B, C, D, Duchamp’s two studio photos that depict his urinal. Carefully note the general blackened area behind the urinal in illustration 41B and 41D and the dark cloth hanging directly behind the urinal in illustration 41A and 41C. Not only do the other photo alterations, as previously discussed, exist in these two studio depictions (remember, the ghost figure in 41A and the likely cutting and pasting of the hatracks and shovels in 41A and B) but the urinal appears to be “applied” to the scene using the classic black background composite technique as the device. Look at our animation analysis in illustration 43A and 43B.

• Illustration 42A
• Illustration 42B
• Illustration 42c
• Illustration 42d

Four 19th century examples of the “black ground method” ofcompositing
multiple photographic images taken at differnet distances

The irregular shadowing, unsure line and edges of the urinal’s silhouette(especially prominent in 43A) indicate a careful but, imperfect, maskingand transfer of the urinal onto the blackground placed in the scene.Note, in the animation, that the studio depictions of the urinal’s interiorlip shape, when outlined, comes very close to matching the form of ourstandard Crane/Mott/Trenton Potteries Bedfordshire model; whereas formof the interior lip on the ideal Stieglitz urinal (that is, when thedrain and pipe holes are corrected to be centered) is very different,see animation 43C. Of course, these data conform with my prediction(derived from my hypothesis) that the two studio photos are slightlyaltered representations of an actual Bedfordshire urinal (and, therefore,that a Bedfordshire model would predictably almost match.) However,a 3D model — even a corrected one — based upon the geometry in Stieglitzphoto would not match either the two studio photo urinals or the Bedfordshiremodel. As I have argued, the Stieglitz image is not representing, factualurinal different from either the 2 studio urinals or Bedfordshire model.I believe that the Stieglitz urinal is a photo composite madeof varied parts taken from photographs of an actual Bedfordshire3D urinal from different perspectives and at different scales).

click images to enlarge
Animations by Gregory Alvarez and Rhonda Roland Shearer

• Illustration 43A
• Illustration 43b
• Illustration 43c

• Video of Urinal animation analysis
  that compares the 3D Crane
  modelto the Stieglitz model
  and this studio photo
• Video of Urinal animation
  analysis that compares the 3D
  Crane modelto the Stieglitz
  model and this studio photo
• Video ofUrinal animation analysis
  that compares the Stieglitz
  photograph,the corrected ideal
  shape and a 3D model (made
  with depicted distortions)are compared.

Looking back at the historical examples of the black background method of photo compositing,in 42C and D (now circled and labeled as illustrations 44A and 44B),we see how the compositing of separate images can play havoc with scale(when we see multiple images of the same figure taken at two differentdistances, we interpret these figures in the final photograph as smalland large sizes.) Other cues reinforce our interpretation of small andlarge figures standing side by side (as opposed to the small figuresuggesting greater distance, and the larger figure as the same sizestanding in the foreground). In illustration 44B, for example, the table’sposition in space (directly opposite to the larger standing figure),along with the feet of the small figure physically happening to meetthe table’s horizontal plane, immediately evokes our most absurd andimpossible interpretation — a real Tom Thumb!

According to forensic experts, the only way to get a better grasp on why and how the scalesof urinal parts, and other objects in the Stieglitz photo look out ofwhack, is to determine as much as possible about actual sizes. For example,how large are the tags used at the 1917 Exhibition? (see illustration45A, of the Stieglitz photo with its tag circled.) The urinal looksdisturbingly small in comparison to the string, hang tag, and wood pedestaltexture. We have already determined, by our prior analysis, that the”ear-brackets” as depicted in the Stieglitz photo appear toolarge when compared to the actual Bedfordshire models of the period.Perhaps the ear-bracket [with the string and tag] are from a singlephoto taken at a different distance, a photo that was then fused withthe rest of the urinal parts?)

Moreover, our forensic expert’s initial analysis echos my suspicion that the urinals in thetwo studio photos (45B, 45C) are, in addition to our sense that thescale of the urinals’ size is off, in comparison to the rest of theroom, most likely composited in, and also do not seem to hang accordingto gravity, (We need to try to measure Duchamp’s old studio room. Ifany original woodwork exists, we can learn a lot more about Duchamp’sphotos.)

click images to enlarge

• Illustration 45A.
• Illustration 45b.
• Illustration 45c.

• Perhaps the ear-bracket
  [with the string and tag] are
  from a single phototaken at a
  different distance which was
  then fused along with the
  rest of the urinal parts.
• The two urinals appear applied upon
  black backgrounds and seem to not
  hang according to gravity.

A closer examination of Duchamp’s 1964 urinal etching shows that, although Duchampdid base his tracings on the Stieglitz photograph to create this etchedimage, he, also and importantly, added a separate and specific extrapart — in a yet another perspective view, more radically differentfrom the rest. Note, when comparing illustration 46A, B and C with 47Aand 47B, the extreme leftward position that the whole urinal would haveto occupy (47B) for us to see this one urinal part in the upper rightside (47A). Why else would Duchamp move so far away from traditionalperspective in one exaggerated and isolated part of this drawing, ifnot from a desire to push his point further, probably because we arelikely not yet again to notice his new rehabilitated perspective systembased upon fusions of multiple points of view in his drawings, modelsor photographs. Remember this etching was done at the end of his life,in 1964. Duchamp had already exposed his new perspective system to theworld since his 1912 Chocolate Grinder painting and no one noticed.Moreover we continue to not notice because the mind creates and dependson such composites of information that Duchamp was presenting as perspectiveall the time.

click images to enlarge

• Illustration 46A
• Illustration 46b
• Illustration 46c

• Stieglitz version of
  Duchamp’s Fountain urinal
• Etching, Marcel Duchamp,
  An Original Revolutionary
  Faucet: Mirrorical Return, 1964
• An overlay of Duchamp’s
  etching (1964) when flopped
  , and placedonto the Stieglitz’s
  photograph of Duchamp’s
  Fountain (1917)
  indicates that used a tracing method.

click each image to enlarge
	click left image to enlarge; click right image for animations
Click to see a video of our animation analysis, comparing the 3D modelmade from the idealized Stieglitz urinal (withoutthe distortions in the original photo) that Duchamp draws with the varied positions that it would have to occupy tomatch the multiple perspective descriptions contained within theetching.
	Illustration 47A	Illustration 47B
	Videoof Urinal animation analysis based on the 1964 etching. Note: Extra perspective part Duchamp added to Stieglitz urinalimage for his Etching, as well as how far turned to the left,the urinal would have to be turned to see the perspective viewof this added part. (Animation created by Gregory Alvarez and Rhonda Roland Shearer.)

Given Duchamp’s claimthat he studied the entire section on perspective at the Paris’s mainlibrary, and that, it is a “no-brainer” to trace the basicshape of the Stieglitz urinal without mistakes, it would be difficultto believe that this extra and distinct perspective part added by Duchampto his urinal etching, would have occurred through accident or incompetence.We are especially encouraged to conceive of Duchamp’s extra perspectivepiece as intentional, since the rest of the etching captures the spatialrelations of the Stieglitz photo so well, including the pipe hole offsetto the left, and so forth.

I must add one finalpoint to buttress my case about the urinal. In the quotation on perspectivethat I cited at the beginning of this essay, Duchamp claimed that headded language, in addition to anecdote, in his rehabilitated form ofperspective. Bonnie Garner suggested that when Duchamp signed his urinalMutt, he, in effect, communicated linguistically the same structurethat he used geometrically (with his fusing of multiple perspectiveparts into one whole). For what else is a “mutt” than an entiremongrel dog composited of many dog breeds (or parts) put together intime — an entity that only appears to be, in a traditional perspective,a low quality whole.

click to enlarge

Illustration 48
Cover of The Blind Man, No. 2: P.B.T., 1917.
Just as Duchamp did with the Urinal, Duchamp combined the ChocolateGrinder with the title of the journal, The Blind Man.

The other colloquialdefinition of mutt as “a stupid person” brings me backto thoughts about the first appearance of Duchamp’s urinal in TheBlind Man (1917). Not only was the Mutt urinal essay and image placedunder The Blind Man heading, but Duchamp and his close friendsalso(and, I believe, not coincidentally) used Duchamp’s ChocolateGrinder painting on the front cover, under The Blind Manbanner, as well — see illustration 48.

I argue that thisplacement of the Chocolate Grinder painting with the BlindMan heading relates directly, in meaning, to Duchamp’s similar positioningof his urinal. For as spectators in 1917, we would have been specificallyblind to Duchamp’s new rehabilitated perspective used in bothhis Fountain urinal and Chocolate Grinder forms,as well as generally blind, as a consequence our foolish dependence(as Duchamp believed) on conventional perspective and “retinalvision” for determining factual reality.

My discovery that the strangely distorted Chocolate Grinder uses the same systematic characteristic approach also found in the hatrack, coatrack and urinal (and a large set of other examples not discussed in this essay) returns us to Duchamp’s words that I used at the beginning of this essay — a quotation that now bears repeating.

Duchamp:  Perspective was very important. The “Large Glass” constitutes a rehabilitation of perspective, which had then been completely ignored and disparaged.
For me, perspective became absolutely scientific.
Cabanne:  It was no longer realistic perspective.
Duchamp:  No. It’s a mathematical, scientific perspective.
Cabanne:  Was it based on calculations?
Duchamp:  Yes, and on dimensions. These were the important elements. What I put inside was what, will you tell me? I was mixing story, anecdote (in the good sense of the word, with visual representation, while giving less importance to visuality, to the visual element, than one generally gives in painting. Already I didn’t want to be preoccupied with visual language. . . .
Cabanne:  Retinal.
Duchamp:  Consequently, retinal. Everything was becoming conceptual, that is, it depended on things other than the retina.

Duchamp’s claims inthis interview (albeit cryptically) that he has done something rigorousand different to rehabilitate perspective, and that he has embodiedthis novelty in his new geometry in the Large Glass — with theChocolate Grinder as one part!

In 1956 Duchamp stated”I was already beginning to make a definite plan, a blueprint forthe Large Glass. All of this was conceived, drawn, and on paperin 1913-14. It was based on a perspective view, meaning a complete knowledgeof the arrangement of the parts. It couldn’t be haphazardly done orchanged afterwards. It had to go through according to plan, so to speak.”In the Cabanne interview Duchamp further claims that “I had workedeight years on this thing, (the Large Glass) which was willed,voluntarily established according to exact plan. . .”

Duchamp carefully provided us with his “Sears Roebuck-like” catalogue of notesand drawings describing his Large Glass project. Mostly writtenbetween 1911-15, these notes include a separate plan view and a sideelevation of the lower “bachelor half” of the Large Glass,(but no 3-D model) and a perspective drawing illustrating measurementsat 1/10 scale of the final Large Glass work, see illustration 49 A, B, C, D.

click images to enlarge

• Illustration 49A
• Illustration 49b
• Illustration 49c
• Illustration 49d

• Perspective view, The Bride Stripped Bare by Her Bachelors, Even, 1915-23
• Plan section of Bachelor Apparatus: Facsimiles of Plan and Elevation, 1913/1934
• Elevation section of Bachelor Apparatus: Facsimiles of Plan and Elevation,1913/193
• Perspective drawing, The Bride Stripped Bare by Her Bachelors, Even, 1913

Architects or engineersdepend upon similar plan views and side elevations as Duchamp’s Bachelorhalf to manufacture 3-D projects and small scale 3-D models. As discussedearlier, perspective drawings, in contrast, indicate the relative positionof a particular observer in visual relation to the object or building.A “precise and exact aspect” in the science of perspective(an “aspect” that Duchamp said he was interested in following),dictates that the perspective in the lower half of the Large Glassdrawing should relate to the geometry of the “blueprint” planand elevation. In other words, if you make a 3-D model following Duchamp’splan view and side elevation blueprints, you should readily be ableto find and replicate the perspective view that Duchamp depicts in hisperspective drawing by using this very same 3-D model.

Most Duchamp scholarshave either accepted or praised Duchamp’s perspective skills. The problemremains, however, that I and a few other scholars have actually made3-D models from Duchamp’s plans — and none of us can find any oneperspective projection view that matches Duchamp’s perspective drawings!Moreover, the process of trying to recreate the Large Glass perspectivedrawing from what a viewer would see of the 3-D model via perspective(equivalent to what one eye or camera lens sees) quickly becomes maddening.When you fit one part of the Large Glass model to its projectionin Duchamp’s perspective drawing (say; part A, the ellipse in one wheelof the Chocolate Grinder, for example — see illustration 49A),the rest (parts B through Z) immediately fall out of place. We losethe fit of part A, and all the other parts C through Z, once part Bis matched — etc.

We may then be temptedto somehow change the plans so that the perspective projection, as laidout in Duchamp’s actual Large Glass, can be generated from the3-D model (built from the plan and elevation view) — which is, in fact,what some scholars have done. But that’s cheating, and such a providencealso assumes that Duchamp was incompetent, or did not care about accuracyof perspective, although he claimed otherwise in earlier interviews,as well as to Cabanne.

If both the plan viewand side elevation construct a consistent 3-D model of the ChocolateGrinder and the overall Large Glass itself, how and why haveI and other scholars failed to generate a similar, if not exact, perspectivedrawing from this 3-D Large Glass model? I will argue that thereason why we cannot generate a single perspective view (in duplicating,what should has been the process that Duchamp followed to create hisperspective drawing) must be Duchamp himself did not used perspectivegeometry, but, rather his new rehabilitated perspective — the methodthat created his perspective drawing and the Large Glass (a.k.a.The Bride Stripped Bare by Her Bachelors, Even 1915-23.)

click to enlarge

Illustration 50A
Cube seen in 2D parts
as eye moves around it

Illustration 50B
Perspective distortions
of cube in relation
to fixed eye

If we analyze theparts of the Large Glass (a 2D perspective view), using a 3Dmodel constructed from Duchamp’s plans, we can only duplicate the depictionsin what is rendered in Duchamp’s Large Glass 2D perspective drawingwhen we move our eye in time around the Large Glass 3D modelto collect snapshots (cuts), and then fuse these separate perspectiveparts together into one depiction — the very same method that Duchampuses in his coatrack, hatrack and urinal 2D representations. Recallthe illustrations (now #50A,B) showing the different perspective depictionsresulting from 4 different fixed eye positions, in contrast to an eyethat moves around a cube.

Illustration 51A,B, C present three animations from our analysis of Duchamp’s ChocolateGrinder and Large Glass in 2D and 3D. The first animation(51A) shows the camera’s perspective while moving around a 3D modelof the Chocolate Grinder in 3D space. Colors highlight the partthat corresponds to the equivalent section of the 2D Chocolate Grinderin the Large Glass perspective drawing. In other words, the animationshows a position that both the camera and 3D Chocolate Grinderwould have to occupy to create the particular 2D Chocolate Grinderpart shown in color code.

click each image and see animations
Illustration 51A	Illustration 51B	Illustration 51C
Threeanimations from our analysis of Duchamp’s Chocolate Grinderand Large Glass in 2D and 3D (created by Gregory Alvarez and Rhonda Roland Shearer)

click to enlarge
Illustration 51D 3D model	Illustration51E 2D composite
Dueto perspective constraints, we would have to move one eye or lensin 3D space and time approximated 43 times around the 3D modelto actually see the same information as Duchamp shows us in hisLarge Glass work in only one instant.(Created by GregoryAlvarez and Rhonda Roland Shearer

The next animation,51B, shows our 3D computer model of the Chocolate Grinder asfundamentally based upon Duchamp’s 1913/1934 plan view and side elevationplans. The animation further depicts how the position of the cameradetermines the particular set of distortions seen by the lens in anyone 2D snapshot of the 3D Chocolate Grinder. Moreover, this animationdepicts that once one camera position allows a match in one part ofthe Chocolate Grinder, the other parts of the Chocolate Grinderand the Large Glass depart from this single perspective position.When other Chocolate Grinder parts are matched, each exists inits own perspective framework. Our efforts to tame all ChocolateGrinder parts into one perspective view, slips hopelessly away witheach successful match of a single part, and the consequent completerejection of the rest in lock step.

The next animationsequence, 51C, illustrates the cut and paste method that Duchamp probablyused to create not only his Chocolate Grinder (and also his coatrack,urinal, hatrack, etc.), but the entire bottom half of the Large Glassitself. As any one photograph yields a single perspective view (withits own particular distortions), Duchamp’s selection of one part fromeach snapshot, after he pastes them together, creates a multiple fusionof varying perspectives. The last frame, showing the Large Glassin color coding, indicates each of the (approximately) 43 parts thatlive in their own perspective world, see Illustrations 51D and 51E.Due to perspectiveconstraints, we would have to move one eye or lens 43 times in 3D spaceto actually see the same information that Duchamp shows us in his singleLarge Glass work! Illustrations51F and 51G map the 43 camera positions in relation to the LargeGlass 3D model that produced the 2D color coded projections in 51Dand 51E.

click to enlarge
Illustration 51F	Illustration 51G
Sideview of set of 43 possible camera positions Duchamp used to createhis Large Glass fusing approx 43 photo parts cut from photographsin 43 different perspectives.	Topdown view of set of 43 possible camera positions Duchamp usedto create his Large Glass fusing approx 43 photo partscut from photographs in 43 different perspectives.

Duchamp’s Revolutionary Alternative
in the context of competing optical experiments

Within the larger Victorian framework of technological mania, the human desire to developa better system of representation for expressing how we see the worldevolved into a frenzy of public interest and private invention. Theadvent of stereoscopic drawings quickly led to a whirl of experimentsamong the expanding developments in stereo photography and moving pictureimages. Stereoscopic devices depend upon the mind’s ability to fusetogether two 2D images that, when seen side by side at the same time,create an impressive 3D effect. (One 2D image is drawn and seen in theperspective of the left eye, and the second 2D image rendered and thenseen when displayed in the position of the right eye). Seemingly endlessvariants and extensions of stereoscopic concepts and equipment weredeveloped and patented into the early 20^th century. The useof various prisms, or mirror systems, in numerous combinations, ledto even more unusual attempts to create stereo fusion with, for example,the use of three images, instead of two, for two eyes. (See illustrations52A,B,C,D,E and F.)

Stereoviewers were all the rage in the late 19th, early 20th century Click each image to enlarge
Illustration 52A	Illustration 52B	Illustration 52A
Stereo viewers were used for entertainment and education around the world.	Saugrin Album Magique French made Stereo-Viewer and book with cards in one gadget.	Hundreds of different Stereoviewers were patented throughout the world; many types are here on this book cover. Paul Wing, Stereoscopes, The First One HundredYears, 1996
Illustration 52D Stereo effect created with Prisms	Illustration 52E 90º Mirror system creates stereo effect	Illustration 52F
Various prism and mirror systems were tried to stretch and test the limitsof what was possibile in creating stereovision.		This unusual optical devise uses three images instead of two!

The limitations ofhuman perception and cognition lie at the center of our illusionaryexperiences evoked by 3D stereo vision or even by “moving pictures,”where projections of film, when speeding by fast enough, appear continuousbecause our eyes and minds are, literally, too weak to detect separationsbetween the 2D images. Moreover, it requires no great leap, for someoneas intelligent as Duchamp, to understand that these 19^thcentury optical experiments expose not only this retinal weakness, but(and more importantly) also suggest, in general, how perception andcognition work. We learn that our eyes and minds take bits of information(from the past and present) and seamlessly fuse them together. However,what we actually think we see, unless we become directlyanalytical and override this automaticity,is much more dominated by a mental construction than we consciouslyrealize.

For example, when we view a depiction of a cube, we are essentially guessing that this object is a cube, basedupon both the direct information that we have in illustration 53 andupon prior experience. The idealized construction of”cubeness” in our minds completely erases the additional informationof the cube thatour two eyes literally see. In illustrations 54A,B, and C, twoviews of the same cube are separately represented as seen by the leftand right eyes (54A,B), whereas 54C is the amount of information thatboth eyes actually see. Illustration 54D shows a schematic plan (inbird’s eye view) of two eyes’ field of vision and fusion when lookingat a cube.

click to enlarge
Illustration 53	Illustration 54 A,B,C	Illustration 54D
We are guessing that this is a cube based upon direct perceptionand prior experience.	Both eyes see A and B as C when fusion occurs.	Bird’s eye view of two eyes looking at cube, two eyes see more informationin sterevision, than in one eye perspective.

We obviously see moreinformation with stereovision’s two eyes than in photography and perspective’s”one-eyed vision.” The mind’s action of fusing two 2D imagesinto a single 3D experience has also raised the dimension of our perceptionand, therefore, also increases the information available to our senses,as shown in illustration 54C. Not everyone possesses the ability tosee representations in stereo. Severe astigmatism, or blindness in oneeye makes the 3D fusion of two 2D images impossible. In early bookson stereo vision, 19^th century experiments that tested thepossibility of an optical device that would allow a single 2D imageto be seen as 3D with only one eye were cited and ridiculed as obviouslyfated to fail. The research of Stephen Jay Gould and me reveals thatDuchamp himself was the first person, even before any scientist succeeded,to develop a system and a device (1923) that produced a 3D stereo fusionin the mind with a single 2D image seen by a single eye. Try the InteractivePresentation in illustration 55. Duchamp’s Rotorelief Discs (1935)surprisingly produce an even greater 3D effect when seen by one eyethan by two. Click on any disc to select. Control speed by clickingon bar and dragging bar up and down (with depressed clicks) betweenfast and slow. Duchamp first made his Rotorelief Discsfor phonographic record playing speeds, 78 or 33 3/1.

Click here for Interactive Presentation

Illustration 55.

Duchamp’s Rotorelief Discs (1935) (machine modeled after 1964 version created by Vittorio Marchi and Robert Slawinski)

Duchamp created many other experiments using stereoscopicpairs. He included two examples in his Boîte-en-Valiseminiature museum (Figs. 56A and 56B). These two stereoimages weremade by Duchamp in 1918 and 1920 but not published until 1941.As I discussed at the Harvard symposium Methods of Understandingin Art and Science: The Case of Duchamp and Poincaré, Duchamp’spreviously unrecognized stereo experiments, as detectedby my studies, include one work, the Wanted Poster (1921),that was (since 1941) viewed as a “readymade” object thatDuchamp only altered by personalizing the object with photos andtext referring to himself. (See illustration 57A and 57B, theWanted Poster print, first seen by spectators in the Boite-en-Valise(1941), as the original Wanted Poster (1921) work is “lost.”

Click each image to enlarge
Illustration 56A	Illustration 56B
Stereo pair (1920) included as print in 1941 Duchap’s Boite-en-valise	Stereo pair made in 1918, also included as print in Duchamp’s Boite-en-valise, 1941

click to enlarge

Illustration 57A
Duchamp Wanted Poster (1921) printed in 1941 Boite-en-valise

Illustration 57B
Wanted Poster detail,
Duchamp’s underground
stereo experiment can be
seen when this detail is placed
into a stereo viewer.

Illustration 57C
The Hyper-Cube represented stereoscopically (Benham)

I noted that the redand blue colored boxes and the two portrait photos (of what may be,even in Duchamp’s original photo source used to recreate his work, aretouched composite of Duchamp and someone else — a criminal perhaps?)are asymmetrically placed and shaped. In other words, the left Duchampimage is higher than the right image, and the lines of the boxes themselvesare strangely designed to be uneven. I noticed one day that both thesize and the separation between the 2 boxes seemed similar to a commonstereo card. I scanned, printed and then cut off the top of the WantedPoster at a duplicate size in the Boîte-en-Valise folder(56B) and then placed it in to a stereo viewer. When seen in stereo,the two asymmetrically shaped boxes in the Wanted Poster unexpectedlyfuse into one symmetrical box. I now could see a single Wanted Posterimage of Duchamp’s head that allowed me to see the front and side ofhis head all at once — a single viewpoint that would not be possiblefor 3D eyes in 3D space. This visual result, I believe, expresses Duchamp’sverbally stated interest in extending a continuum to include transformationsamong 2, 3 and 4 dimensions. (See illustration 58, showing atraditional stereo card that reflects the popular and technical interestin 4D space and objects in the early 20^th century. This 2Dstereopair, as seen here, depicts a 4D figure in two different perspectiveviews. When seen in a stereo viewer, the dimension will then be increasedinto a single 3D view of this same 4D object, also shown in 2D.

Using what Duchamp called a 4D eye [eye⁴], only 4D space allows us to see 3D objects 360° in the round in one instant; whereas, in 3D space a 3D eye (eye³) must move in time around a 3D object to collect 2D observations (thus reducing an object from 3D to a series if 2D shapshots). Only after these cuts are fused together, can we recreate in our minds a sense or approximation of any actual 3D object in the round (thus increasing the dimension when transforming a series of 2D cuts into a 3D object). Duchamp’s note, illustration 59, uses the fist’s ability to hold and experience the form of a 3D object, all at once, as analogous to what would occur in 4D vision. Illustration 60, a portrait photograph of Duchamp, also mimics what could only be simultaneously seen in 4D space. This portrait is also similar to the experience evoked when seeing the two Wanted Poster heads and lined boxes in a stereo viewer. Significantly, Duchamp selected this very photo (60) as the cover for his own catalogue raisonné design in 1958.

click images to enlarge

• Illustration 59
• Illustration 60

• English translation of the Note: “The View3 of a plane P.
  corresponds in the hyperspace to a grasp4 of which one can get an idea by gripping a penknife in the hand, for example”
  Marcel Duchamp, mathematical note from In the Infinitive [a.k.a. the White Box], written in 1910s published in 1967
• Cover design done by Duchamp for his Catalogue Raisonné (1953) includes this portrait photograph that illustrates the similar “4D” effect (seeing front and side view at once) found when placing the Wanted Poster (57B) into a stereo viewer

With Duchamp’s undergroundexperiment in the Wanted Poster, we may have increased our informationwith a 4D experience, but the data provided by Duchamp’s head are stillincomplete. Panoramic painting and photography represented yet another19^th and 20^th century experiment and approachto packing even more 3D information into 2D images. Illustration 61shows a “panoramic” view of a woman’s head. The photo uncomfortablyreads as if a 360° view of the woman’s head were rolled out, like cookiedough, onto a 2D plane. Such a panoramic photograph, by allowing usto see a 3D object (such as a head) on all sides at once, certainlyyields more 3D information in

click to enlarge

Illustration 61
Apanoramic photo of a
woman’s head captures a
whole 3D object in 2D space,
allowing it to be seen all at once.

2D than stereo experimentscan provide, and also offers a perspective of something not possiblein our normal 3D vision in 3D space. Yet, because the distortions producedby the panoramic technique, as seen in illustration 60, are so viscerallyrepulsive (probably because they evoke a sense of seeing flayed skin– the only way to make such a flat geometric view literally possible),and so foreign to our actual experience, we are unable to disregardthe panoramic distortions, whereas we routinely, and without effort,ignore or seamlessly filter out perspective distortions. Therefore,we can conclude that the panorama presents an interesting representationaleffect that would not challenge perspective photography as a dominantor popular convention.

click to enlarge

Illustration 62
Pablo Picasso, Violin
and Grapes, spring
and autumn, 1912

Cubism, in addition to its status as the beginning of one of the two biggest revolutionary departures in art (the other being the advent of perspective itself in the Renaissance), emerged, for Duchamp and others, as yet another experiment and alternative to static perspective representation in the larger cultural context of the early 20^th century (see illustration 61, a cubist painting by Picasso).

* Part IV through VI will be published in Tout-Fait, Perpetual 2005.

Illustrations 2A-2F, 12A-D, 13B, 14A, 15A, 16A, 17, 18A-B, 19A, 20A-C, 21A, 22A-B, 23A-E, 32A, 34A-H, 41A-D, 46B, 49A-D ©2005 Succession Marcel Duchamp, ARS, N.Y./ADAGP, Paris. All rights reserved.